MATH 163, Spring 2001 Due Date: Name(s):
Extra Project 4.5c: Graphing Functions Again
Objective
To get more exercise graphing a function f using its first and second derivatives.
Narrative
If you have not already done so, do Project 4.5b.
In this project we simply provide another example that involves graphing a function f using its first and
second derivatives.
Task
Type the command lines below into Maple in the order in which they are listed. They produce a graph of
the function f(x) = (1 - x2
)/(1 + x2
), and three recording strips below the graph of f.
> # Extra Project 4.5c: Graphing Functions Again
> restart: with(plots):
> f := x -> (1-x^2)/(1+x^2);
> f1 := D(f);
> simplify(f1(x));
> f2 := D(f1);
> simplify(f2(x));
> plot0 := plot({-6,-5,-4,-3,0},x=-6..6,y=-6..3):
> plot1 := textplot({[-6,-3.5,'f'],[-6,-4.5,'f1'],[-6,-5.5,'f2']}):
> display({plot0,plot1});
At this time, make a hard-copy of your input and Maple's responses. Then, ...
a) fill in the recording strips on the graphic you produced using information about f and f , and
b) use the information in the recording strips to sketch the graph of f.